Producers have been filming at a church in the Jungle area, the base for thousands of migrants who are trying to reach Britain illegally, The Sun reported.
The newspaper said the long running series will feature an Ethiopian Orthodox Church, attended by hundreds of people each week.
An estimated 5,000 migrants displaced from countries including Syria, Libya and Eritrea are believed to be camped in and around Calais.
Former Songs of Praise presenter Revd Steve Chalke has urged producers on the programme to stick with the issue, despite the ongoing contrversy.
"We talked to Catholics and we talked to Protestants at the height of some of the IRA troubles, and some people said 'I don't want to be in in this programme, I'm scarred' and that was respected and obviously this church leader's view has been respected. But I'm sure that church leader wants the issue to be known about," said Chalke.
It's thought the full crew for Songs Of Praise, including host Aled Jones, will travel to the site this weekend but the programme will not be broadcast until a later date.
A BBC spokeswoman said: "Songs Of Praise is a magazine-style programme. Each week it brings hymns from churches around the UK and short topical magazine features of interest to Christians from a range of places."
It is understood that the programme will not be a live special, but a standard one following the usual format.
Church in the Jungle camp in #Calais. Dozens of Ethiopian& Eritrean Christians attend service each Sunday. @vicenews pic.twitter.com/8Ro1ro7L9Y
— Sally Hayden (@sallyhayd) August 5, 2015